Our purpose is to study a dual problem: given large \(G\) -representations \(V_i\) , when must \(V_1\otimes V_2\otimes V_3\)  contain all irreducible \(G\) -representations as subrepresentations? In such a case we say this tensor product covers \(\text{Irrep}(G)\) , the set of (isomorphism classes of) irreducible \(G\) -representations. Another line of working on covering \(\text{Irrep}(G)\)  is the Saxl conjecture, which asserts that \(\text{Irrep}(S_n)\)  can be covered by a tensor square for \(n\)  large enough - see [1]}, [2]}, [3]}, [4]}. The work [5]} establishes such a result in groups of Lie type, and [6]}, [7]}, [8]} study the number of tensor powers of a fixed irreducible representation needed to cover \(\text{Irrep}(G)\)  in various cases. As we allow our tensor factors \(V_i\)  to be reducible, it is not obvious how to best measure their size. We will use the Plancherel measure.
